JERUSALEM (CNN) - U.S. envoy George Mitchell met with Israeli President Shimon Peres Tuesday, asking for a prompt resumption of the stalled Mideast peace talks and playing down tensions that have arisen between the two countries in recent days.

"Israelis and Palestinians have a responsibility to meet their obligations under the Road Map," Mitchell said. "And we all share an obligation to create the conditions for the prompt resumption and early conclusion of negotiations."

The 2003 Road Map is a peace plan that calls, among other things, for Israel to halt building settlements in occupied territories and Palestinians to stop violence.

In recent days, the Obama administration has repeatedly called on its Middle Eastern ally to stop construction of settlements and to work toward a two-state solution, with a separate Palestinian state alongside Israel.

In a speech to the Muslim world Thursday, U.S. President Barack Obama said his country "does not accept the legitimacy of continued Israeli settlements."

So far, Israeli Prime Minister Benjamin Netanyahu has refused U.S. calls to stop, and said he will deliver a major speech Sunday in which he will lay out his plan for the country's peace and security.

"Let me be clear. These are not disagreements among adversaries," said Mitchell, who was dispatched to the region to try and kick-start the negotiating process. "The United States and Israel are and will remain close allies and friends."

Peres too tried to calm the diplomatic waters.

"I think (Obama's) address was extremely sensitive, touching, concerning all sides without trying to play one against the other, paying compliments when it was justified, criticizing when it was necessary in the most honest way," he said.